Is there anyway I can get a report directly from Postfix about how many emails were sent per day, or other similar statistics? As a "out of the box" solution?
Mailgraph provides a fairly good overview of the health of your mail system. 


I'm not sure what your "directly from Postfix" requirement is, but I'll offer pflogsumm.pl as an option. It just runs via cron and parses through your mail logs, generating aggregate statistics as it goes. 


I added some postfix stats to ganglia. These are not daily stats, but by the minute stats. Here is my blog post about it. 

